Worksheet on Comparing Quantities

Solved Questions on Comparing Quantities

1. The price of sugar has increased by 30%. What percentage of sugar intake needs to be reduced in order to maintain the same amount spent on sugar?

a) 3¹⁄₁₃%
b) 13¹⁄₁₃%
c) 23¹⁄₁₃%
d) 33¹⁄₁₃%

Answer: c) 23¹⁄₁₃%

Explanation: Let price of x kg of sugar be $100.

The price of sugar has increased by 30%.

Increase in price of sugar = 30% of $100 = (30/100) × 100 = $30

Increased price = $100 + $30 = $130

Consumption of sugar at $130 = x kg

Sugar intake needs to be reduced in order to maintain the same amount spent on sugar.

Consumption of sugar at $1 = x/130 kg

Consumption of sugar at $100 =  (x/130) × 100 = 10x/13

Decrease in consumption = x − 10x/13 = 3x/13

Required % of decrease in consumption =

2. Shakira bought a washing machine for $956.25 including 12.5% value-added tax. What was the price of the washing machine before value added tax was added?

a) $750
b) $850
c) $950
d) $1050

Answer: b) $850

Explanation: Price of a washing machine including value-added tax = $956.25

Let price of washing machine before value added tax was added be $x.

Value-added tax = 12.5% of Price before value-added tax
                         = 12.5/100 × x
                          = $(125x/1000)

Price before value added tax + Value added tax = Price including value added tax
⇒ x + 125x/1000 = 956.25
⇒ (1000x + 125x)/1000 = 95625/100
⇒ 1125x/1000 = 95625/100
⇒ x = [(95625/100) × 1000]/1125
⇒ x = $850

3. A jewellery shop in New York allows a 25% discount on its jewellery and still makes a profit of 25%. What is the marked price of a pair of synthetic ruby earrings that the shopkeeper bought for $500?

a) $833.33
b) $833.66
c) $866.33
d) $866.66

Answer: a) $833.33

Explanation: Cost Price (C.P.) of a pair of earrings = $500

Profit% = 25%

Selling Price (S.P.) of a pair of earrings = [(100 + profit%) ÷ 100] × C.P.
                                                          = [(100 + 25) ÷ 100] × 500
                                                            = (125 ÷ 100) × 500
                                                              = $625 ……………..(1)

Let Marked Price (M.P.) of a pair of earrings be $x.

Discount% = 25%

Selling Price (S.P.) of a pair of earrings = [(100 − Discount%) ÷ 100] × M.P.
                                                          = [(100 − 25) ÷ 100] × x
                                                            = (75 ÷ 100) × x
                                                              = $(^75x⁄₁₀₀) ……………..(2)
From (1) and (2),

^75x⁄₁₀₀ = 625
⇒ x = 625 × ¹⁰⁰⁄₇₅
⇒ x = $833.33

Marked price of a pair of synthetic ruby earrings is $833.33.

4. Mr. Bond borrowed $95000 from a bank at 13% per annum in simple interest and an equal sum from another bank at 6% per annum compounded half-yearly. What is the total interest paid to the banks by Mr Bond in a year?

a) $18105.50
b) $18115.50
c) $18125.50
d) $18135.50

Answer: d) $18135.50

Explanation: In case of Simple Interest:
P = $95000
R = 13% p.a
T = 1 year

S.I. = (P × R × T) ÷ 100
= (95000 × 13 × 1) ÷100
= $12350

In case of Compound Interest:

P = $95000
r = 6% p.a (Compounded half yearly)
t = 1 year

C.I. = A − P
    = 100785.50 − 95000
    = $5785.50

Total interest paid to the banks by Mr. Bond in a year = S.I. + C.I.
  = $(12350 + 5785.50)
  = $18135.50

5. What is the compound interest on $62500 for 6 months at 8% per annum compounded quarterly?

a) $2512.5
b) $2525
c) $2537.5
d) $2550

Answer: b) $2525

Explanation: P = $62500
r = 8% p.a (Compounded quarterly)
t = 6 months = 612 year = ½ year